Problem 44951. Verify Law of Large Numbers

Created by Pooja Lalan

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value of a 6-sided die is</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>3.5</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>, simulate</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1e8</w:t></w:r><w:r><w:t> N-sided dice rolls by creating a vector of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1e8</w:t></w:r><w:r><w:t> uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1</w:t></w:r><w:r><w:t> to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

16129 Solutions
3497 Solvers

Last Solution submitted on Apr 15, 2021

Last 200 Solutions

Problem Comments

9 Comments

9 Comments

Show 6 older comments

David Motson on 12 Nov 2019

The solution quits because it's taking too long. 1e8 is too many?

Stephen Strickland on 28 Mar 2020

The difference should essentially be zero i.e. the two averages equal. I wrote a successful script; run in my desktop environment but the tool won't accept my answer as valid.

Jasmine Bajaj on 11 Apr 2020

It crashes every time, how to complete it?

Charles Abrams on 25 Apr 2020

To get this right apparently you have to generate the random numbers exactly the same way as the answer key. When it tests your script it seeds the random number generator and then confirms whether your program gets EXACTLY the same result. However, if you generate the random numbers in any way different from the key, your answer will be "wrong" but is probably still correct.

Rafael S.T. Vieira on 2 Jun 2020

There is a MatLab function that does it. Nice and easy.

Louis Repussard on 9 Oct 2020

Nice one

Wooseong Choi on 25 Oct 2020

"1e8 N-sided dice" made me confused. I think it should be changed to "1e8-sided dice".

Ryan Chapman on 27 Nov 2020

this problem brakes the website. 1e8 is too big and the website blocks out my computer.

Victor Zarate on 11 Feb 2021

After multiple tries of submitting what i thought the correct answer and being met with "While evaluating the solution, the server encountered an error caused by temporary unavailability of MATLAB Service. Wait a few minutes for the MATLAB Service to return, and then rescore." what seemed to do the trick was what Marcel Dornbusch hinted in his comment.
Just make sure you do not output every bit of information in the code, and just output the answer.

Solution Comments

Solution 5311217

Solution 5164663

1 Comment

1 Comment

Maya Gonzalez on 24 Mar 2021 at 18:33

this one is fun!

Solution 5162063

1 Comment

1 Comment

Manfred Neumann on 24 Mar 2021 at 14:33

It's really confusing, but: you have a dice with N sides! and you roll this dice 1e8 times!
Since I checkt this, the solution was clear ...

Solution 5024526

1 Comment

1 Comment

李君 on 9 Mar 2021

description of this problem is confusing.

Solution 4569343

1 Comment

1 Comment

Sandor Szabo on 10 Jan 2021

Incorrect!
I created a "step by step" solution that was not accepted. Then I reformulated this solution for compound formula end, voila, it was accepted.

Solution 4564648

1 Comment

1 Comment

Alain Daniel Godo Alonso on 9 Jan 2021

I don't know why every time I send the solution the site show me: "While evaluating the solution, the server encountered an error caused by temporary unavailability of MATLAB Service. Wait a few minutes for the MATLAB Service to return, and then rescore."

Solution 4528718

1 Comment

1 Comment

OMKARAM RAJESHWARA RAJU on 2 Jan 2021

function dice_diff = loln(N)
%N-sided dice , 1e8 times rolling
dice_diff =mean(randi(N,1e8,1)) - ((N+1)/2);
end

Solution 3960703

1 Comment

1 Comment

Kriti on 2 Dec 2020

function dice_diff = loln(N)
%the mean of integer from 1 to N
A = 1:N;
meanN = mean(A);
V = randi(N, 1e8,1);
meanvector = mean(V);
dice_diff = meanvector - meanN;
end

Solution 3774598

1 Comment

1 Comment

Lester Goh on 22 Nov 2020

why tho

Solution 2636518

1 Comment

1 Comment

Marcel Dornbusch on 30 Jun 2020

For saving execution time, do without outpout! Then it worked for me.

Solution 2504012

1 Comment

1 Comment

AIJAZ BHAT on 9 Jun 2020

what is the problem with this solution

Solution 2174463

2 Comments

2 Comments

Drake Madison on 25 Mar 2020

Note that using rand() with round() will not produce the correct answer. There is another function that must be used instead.

Gregory Bohorquez on 3 Jul 2020

What can be used? I am a bit confused.

Solution 2167277

1 Comment

1 Comment

Belmont Aurélien on 20 Mar 2020

1e8 is too big for the Matlab website. It crashes every time I try it. I managed to find a solution on the full version so I put it in comments and cheated to pass it.

Solution 2015845

2 Comments

2 Comments

David Motson on 12 Nov 2019

I discovered using a for loop doesn't work - too slow. Then I realised that randi can generate the required vector, doh!

Gabriel Gomes on 19 Mar 2020

Can anyone do that in a size smaller than 22? That was the smallest size I could get.

Problem Recent Solvers3497

Problem Tags

rand random integers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers3497

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers3497

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players